## moongazer Group Title If tan (theta) =5/4 and cos (theta) < 0 . Find the other trig. functions. Could someone check my answers? 2 years ago 2 years ago

1. moongazer Group Title

am I right that theta is in quadrant 3 ?

2. Silent_Sorrow Group Title

Yup, so Sin (theta) < 0 as well

3. moongazer Group Title

4. waterineyes Group Title

5. moongazer Group Title

ok

6. moongazer Group Title

$\sin \theta =(-5\sqrt{41})/41$ $\cos \theta = (-4\sqrt{41})/41$ $\tan \theta = 5/4$ $\csc \theta = -\sqrt{41}/5$ $\sec \theta =-\sqrt{41}/4$ $\cot \theta = 4/5$

7. moongazer Group Title

Am I correct?

8. Silent_Sorrow Group Title

|dw:1341743660142:dw| Just remember "All Science Teachers Crazy" so in the first quad all trig functions are positive, in the 2nd all Sine functions are positive, in the 3rd all Tangent functions are positive so in the 4th all Cosine functions are positive.

9. moongazer Group Title

10. moongazer Group Title

Could someone check it?

11. moongazer Group Title

12. mathslover Group Title

when cos theta is negative then theta lies in 2nd quadrant ..

13. moongazer Group Title

@mathslover why?

14. mathslover Group Title

15. moongazer Group Title

ok thanks :)

16. mathslover Group Title

Remember this :Quadrant 1: Cosine is positive and Sine is positive. (x > 0 ; y > 0) just as ( cos(theta) > 0 ; sin(theta) > 0) Quadrant 2: Cosine is negative and Sine is positive. (x < 0; y > 0) just as ( cos(theta) < 0 ; sin(theta) > 0) Quadrant 3: Cosine is negative and Sine is negative. (x < 0 ; y < 0) just as ( cos(theta) < 0 ; sin(theta)< 0) Quadrant 4: Cosine is positive and Sine is negative. ( x > 0 ; y < 0 ) just as ( cos(theta) > 0 ; sin(theta) < 0)

17. mathslover Group Title

@moongazer

18. moongazer Group Title

I am here

19. mathslover Group Title

So did u get that quadrant 2 : cos theta is negative ?

20. moongazer Group Title

21. mathslover Group Title

Take ur time

22. moongazer Group Title

But in quadrant 3 cos theta is also negative so why I can't choose it as the location of theta?

23. moongazer Group Title

isn't it that tan theta is positive in quadrant 3 and according to the given tan theta is positive. So choosing that theta is in quadrant 3 is better?

24. mathslover Group Title

oh yes u r also right but i am not perfect in this topic may be @lalaly do it for u

25. moongazer Group Title

@lalaly My answers are correct right?

26. lalaly Group Title

u can describe this as a right triangle $\tan (\theta)=\frac{opposite}{adjacent}=\frac{5}{4}$so from this u know that opposite=5 and adjacent =4 |dw:1341746704835:dw|

27. lalaly Group Title

now use those values to find the ratios for the other trig functions

28. moongazer Group Title

But isn't it I can also view as|dw:1341747710304:dw|

29. moongazer Group Title

Are my answers right or wrong?

30. ash2326 Group Title

@moongazer you are correct :D

31. moongazer Group Title

@ash2326 Thanks for that!

32. ash2326 Group Title

you wanna see, the pic I made to check this?

33. moongazer Group Title

ok, let me see it :)

34. ash2326 Group Title

here it is

35. moongazer Group Title

That is also what I am thinking :)

36. ash2326 Group Title

Yay:D